Question

A car is accelerating uniformly as it passes two check points which are 30 meters apart. the time taken between checkpoints is 4 seconds and the car speed at the first checkpoint is 5m/s. the car's speed at second checkpoint is

Answer 1

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Answer 2

Given,

Distance between the two checkpoints = 30 meters

Time taken in traveling between the two checkpoints = 4 seconds

Speed of the car at the first checkpoint = 5m/s

To find,

The speed of the car at the second checkpoint.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume that the speed of the car at the second checkpoint is x m/s and its acceleration is a m/s^2.

Mathematically, according to the laws of linear motion;

For a body moving along a distance (s) with initial velocity (u), final velocity (v), acceleration (a), and time of travel (t),

(I) v = u + at

(II) s = ut + 1/2(at^2)

(III) v^2 = u^2 + 2as

{Statement-1}

Now, according to the question;

For the car accelerating uniformly as it passes two checkpoints;

Distance covered (s) = distance between the two checkpoints = 30 meters

Initial velocity (u) = speed of the car at the first checkpoint = 5m/s

Final velocity (v) = speed of the car at the second checkpoint = x m/s

Time of travel (t) = 4 seconds

Now, according to statement-1 (II);

s = ut + 1/2(at^2)

=> 30 m = (5 m/s)(4 s) + (a/2)×(4s)^2

=> a × 8 s^2 = 30 m - 20 m = 10 m

=> a = 10/8 = 1.25 m/s^2

=> acceleration of the car = 1.25 m/s^2

Now, according to statement-1 (I);

v = u + at

= 5 m/s + (1.25 m/s^2)(4 s)

= 5 m/s + 5 m/s

=> x = 10 m/s

=> speed of the car at the second checkpoint = 10 m/s

Hence, the speed of the car at the second checkpoint is equal to 10 m/s.