Distance-Time Graph Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following options represents the distance-time graph of a stationary object?

Ans. The correct answer is option (d)

Explanation: Because a stationary object does not move, the graph in option (d) is the right answer.

Ques. The below graph represents a distance-time graph with uniform velocity.

1. True
2. False

Ans. The correct answer is a. True

Explanation: When a body travels the same distance in the same amount of time, it is said to have uniform velocity.

Ques. The distance-time graph shows a curved line in which type of motion?

Ans. The distance-time graph for non-uniform motion is not a straight line since speed varies; instead, it might be a curve or a zigzag line.

Ques. The slope of a distance-time graph represents

1. Acceleration
2. Velocity
3. Displacement
4. Speed

Ans. The correct answer is d. Speed

Explanation: The gradient of a distance-time graph is equal to the speed indicated by a straight line.

Ques. In a distance-time graph, which variable is plotted on the Y-axis?

1. Distance
2. Speed
3. Velocity
4. Time

Ans. The correct answer is a. Distance

Explanation: Distance is drawn on the y-axis and time is plotted on the x-axis in a distance-time graph.

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Short Answers Questions [2 Marks Questions]

Ques. What is a graph?

Ans. A graph is a diagram that depicts the relationship between two variables, often measured along one of a pair of axes at right angles.

Ques. What are the three basic types of graphs?

Ans. The three basic types of graphs are

• Line graphs
• Pie graphs
• Bar graphs

Ques. What is meant by a distance-time graph?

Ans. A distance-time graph depicts how far an object has gone in a given time. It is a basic line graph that depicts distance against time information. Distance is displayed on the Y-axis, while time is drawn on the X-axis.

Ques. What are the types of motion in a ceiling fan and its blade? Is it the same?

Ans. No, the total movement of a fan is distinct from the movement of the fan blades alone. Ceiling fans "rotate" on their axis, so we may call them rotational motion, whereas fan blades move in a circle with a defined radius from the center, thus they are circular motion.

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Long Answers Questions [3 Marks Questions]

Ques. What are the characteristics of the distance-time graph?

Ans. The characteristics of distance-time graphs are determined by the type of motion represented.

For Uniform motion:

• A straight line is depicted on the graph.
• The slope of the line is equal to the object's speed.
• The faster the object moves, the greater the slope of the line.

For Non-uniform motion:

• The graph is a curved line.
• At every point along the curve, the slope equals the speed of the object at that moment.
• The body is accelerating if the slope of the curve is positive.
• When the slope of the curve is negative, the body is slowing down.

Ques. What are the applications of the distance-time graph?

Ans. The following are the applications of the distance-time graph

• In physics, distance-time graphs are used for studying the motion of things such as vehicles, trains, and airplanes. They may be used to calculate an object's speed, acceleration, and deceleration, as well as the distance traveled in a certain amount of time.
• Engineers use distance-time graphs to develop and optimize transportation systems such as roads, trains, and airports. They are also useful for designing and controlling machines and robotics.
• Distance-time graphs are used in sports to analyze athlete performance. They can, for example, be used to calculate a runner's speed at various stages throughout a race or the acceleration of a swimmer at the start of a race.

Ques. When a ball is thrown vertically upwards, it reaches a maximum height of 5 m. The initial velocity of the ball was?

Ans. Let u be the initial velocity of the ball.

At maximum height, the final velocity of the ball becomes zero, i.e. v = 0

Given the maximum height of the ball, S = 5 m

Since the motion is under constant acceleration and the acceleration is provided by the acceleration due to gravity (g).

Using the equation of motion v² = u² + 2aS

Here 

• S = 5 m
• v = 0
• a = – g = – 10 m/s²

On substituting the values, we get

u² = – 2 x (-10) x 5 = 100

⇒ u = 10 m/s

Hence the initial velocity of the ball is 10 m/s.

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Very Long Answers Questions [5 Marks Questions]

Ques. When two particles A and B are at point O, A is moving with a constant velocity of 50 m/s, while B is not moving. But B possesses a constant acceleration of 10 m/s². After how much time they will be at a distance of 125 m?

Ans. For particle A

• The initial velocity, u_A = 50 m/s
• Acceleration, a_A = 0

For particle B

• The initial velocity, u_B = 0
• Acceleration, a_B = 10 m/s²

The initial velocity of particle A with respect to particle B is given by

u_AB = u_A - u_B

⇒ u_AB = 50 - 0 = 50 m/s

The acceleration of particle A with respect to particle B is given by

a_AB = a_A - a_B

⇒ a_AB = 0 - 10 = – 10 m/s²

The distance between particle A and B after time t is given by

S_AB = u_ABt + 1/2 a_ABt²

Given SAB = 125 m

On substituting the values, we get

125 = 50t - 1/2 x (-10)t²

⇒ 125 = 50t - 5t²

⇒ 5t² – 50t + 125 = 0

⇒ t = 5 seconds

Hence both the particles will be at a distance of 125 m at time t = 5 seconds

Ques. Rama went for a drive in his car. The distance-time graph shows her full journey. Thus, determine the total distance traveled during her journey, along with her average speed between 4:30 and 5:30.

Ans. Rama traveled 30 km from her home. She drove 20 km after pausing for a time. She then abruptly came to a halt, driving 50 km back home after beginning her excursion.

The total distance traveled by the Rama = 30 + 20 + 50 = 100 km

The two large squares total 30 minutes, according to the axis shown in the graph.

This means that one large square takes 15 minutes to complete. That means Rama is at rest from 4:30 to 4:45.

Between 4:30 and 4:45, the speed is 0/0.25 = 0 km/h.

The slope of the graph between 4:45 and 5:00 must be calculated in order to establish.

Rama's average speed between 4:30 and 5:30. This particular time lasted 15 minutes, which is equal to 0.25 hours. It may be stated as "change in x".

During this time, she extended her distance from home from 30 to 50 km.

Hence, she traveled 20 km in total, which is also known as the "change in y." 

As a result, slope = 20/0.25 = 80 km/h.

Therefore, the average speed is (0 + 80)/2 = 40 km/h.

Ques. A stone is thrown vertically upwards. On its way, it passes point A with a speed v and passes point B, 30 m higher than A, with a speed v/2. Find

1. The speed v
2. The maximum height reached by the stone above point B.

Ans. Let us choose the positive direction along vertically upward.

1. Between the point A and B, using the equation of motion v² = u² + 2aS, we get

(+v/2)² = (+v)² + 2(-g)(+30)

⇒ v²/4 = v² - 588

⇒ v² = 784

⇒ v = 28 m/s

2. The speed at B = v/2

On substituting the value of v on the above equation, we get

The speed at B = 28/2 = 14 m/s

Again using equation v² = u² + 2aS between B and C, we get

0 = (14)² - 2(9.8)S

⇒ S = 10 m

Therefore, the maximum height attained above B is 10 m.

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