Question

How will you show that the slope of displacement-time graph gives velocity of the body?

July 23, 2024

Answer

The adjoining figure shows the displacement-time graph

for a body moving with uniform velocity. It covers

distance s₁and s₂at times t₁and t₂respectively.

Slope of line PQ = tan θ = $QR \over PR$

= $s_2- s_1 \over t_2 - t_1$ = $Displacement \over Time$

As $Displacement \over Time$ is velocity, it y, so the slope of the distance-time graph gives velocity of the body.

💡 Some Related Questions

The table given below shows distance (n cm) travelled by bodies A, B and C. Read this data carefully and answer the following questions. Distance (in cm) covered by different bodies.

Time in (s) Body (A) Body (B) Body (C)

1stSecond 20 20 20

2ndSecond 20 36 60

3rdSecond 20 24 100

4thSecond 20 30 140

5thSecond 20 48 180

(i) Which of the bodies is moving with (a) constant speed? (b) constant acceleration? (c) non-uniform acceleration? (ii) Which of the bodies covers (a) maximum distance in 3rd second? (b) minimum distance in 3rd second?

Suppose a squirrel is moving at a steady speed from the base of a tree towards some nuts. It then stays in the same position for a while, eating the nuts, before returning to the tree at the same speed. A graph can be plotted with distance on the x-axis and the time on y-axis.

Observe the graph carefully and answer the following questions. (i) Which part of the graph shows the squirrel moving away from the tree? (ii) Name the point on the graph which is 6 m away from the base of the tree. (ii) Which part of the graph shows that the squirrel is not moving? (iv) Which part of the graph shows that the squirrel is returning to the tree? (v) Calculate the speed of the squirrel from the graph during its journey.

A girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position. Her displacement-time graph is shown in figure. Plot a velocity-time graph for the same.

Four cars A, B, C and D are moving on a levelled road. Their distance versus time are shown in figure. Which car is the slowest?

The driver of train A travelling at a speed of 54 kmh-1 applies brakes and retards the train uniformly. The train stops in 5 seconds. Another train B is travelling on the parallel with a speed of 36 kmh-1 . Its driver applies the brakes and the train retards uniformly; train B stops in 10 seconds. Plot speed-time graphs for both the trains on the same axis. Which of the trains travelled farther after the brakes were applied?

Two stones are thrown vertically upwards simultaneously with their initial velocities u1 and u2 respectively. Prove that the heights reached by them would be in the ratio of $u_1^2 : u_2^2$ . (Assume upward acceleration is -g and downward acceleration to be + g).

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between 4th and 5th seconds.

Deduce the following equations of motion: (i) s = ut + ( 𝟏/𝟐 )at2 (ii) v2 =u 2 + 2as

with the help of a graph, derive the relation v = u + at.

Given below is the velocity-time graph for the motion of the car. What does the nature of the graph show? Also find the acceleration of the car.