Name: Equations of Motion Using Graphs
Uploaded: 2019-07-19
Duration: 9 min 14 s
Description: Equations of motion help us solve numerous problems and predictions related to motion. Let us understand their derivation using graphs in this video.

Question

A driver of a car traveling at

52 k m / h

applies the brakes and accelerates uniformly in the opposite direction.The car stops in

5 s .

Another driver going at

3 k m / h

in another car applies his brakes slowly and stops in

10 s .

On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?

Accepted Answer

For the first car:

The initial speed of the car, $u_{1} = 52 km / h = \frac{52 \times 1000}{3600} = 14.4 m / s$ .

Time taken to stop the car, $t_{1} = 5 s$ .

The final speed of the car becomes zero $5 s$ after application of brakes.

For the second car:

The initial speed of the car, $u_{2} = 3 km / h = 0.8 m / s$ .

Time taken to stop the car, $t_{2} = 10 s$ .

After the application of the brake, the final speed of the car becomes zero after $10 s$ .

The plot of the speed versus time graph for the two cars is shown in the following figure:

We know that the area under the speed-time graph will give distance covered in the time interval.

$Distance covered by the first car = Area under the graph line PR = Area of triangle OPR = 1 / 2 \times 5 \times 14.4 = 36 m$
$Distance covered by the second car = Area under the graph line SQ = Area of triangle OSQ = 1 / 2 \times 10 \times 0.8 = 4 m$
We can see that

$Area of triangle OPR > Area of triangle OSQ$

Hence, the distance covered by the first car is greater than the distance covered by the second car.

Important Questions on Motion

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