Question

A truck starts from rest with an acceleration of 1.5 m per second square while a car 150 M behind starts from rest with an acceleration of 2 metre per second square. how long will it take before both the truck and car are side by side?

Answer 1

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In the picture!

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Answer 2

Time taken before both the truck and car are side by side is 24.5 sec

Given : A truck starts from rest with an acceleration of 1.5 $m/s^{2}$

A car 150 m  behind starts from rest with an acceleration of 2  $m/s^{2}$

Distance between car and truck is 150 m

To Find : Time taken before both the truck and car are side by side

Solution : Time taken before both the truck and car are side by side is 24.5 sec

It is given the a truck starts from rest with an acceleration of 1.5 $m/s^{2}$ and

a car 150 m  behind starts from rest with an acceleration of 2  $m/s^{2}$

we have to find the time taken before both the truck and car are side by side

Now initial velocity of truck ut = 0 m/s

Acceleration of the truck is 1.5 $m/s^{2}$

Initial velocity of the car is uc = 0 m/s

Acceleration of the car is 2 $m/s^{2}$

Distance between car and truck (s) is 150 m

Let distance covered by truck in time t is s m 'and

the distance covered by the car in time t is s+150 m

Using second equation of motion

$s = \frac{1}{2}at^{2}$

Applying second equation of motion for truck

s = $\frac{1}{2}1.5(t^{2})$

s = $\frac{3}{4}t^{2}$   ---- 1)

Applying second equation of motion for car

s +150 = $\frac{1}{2}2(t^{2})$

s +150 = $t^{2}$

Putting the value of s from equation 1) we get

$\frac{3}{4}t^{2}$ +150 =  $t^{2}$

150 = $\frac{1}{4}t^{2}$

$t^{2}$ = 600

t = $\sqrt{600}$

t = 24.5 sec

So time taken before both the truck and car are side by side is 24.5 sec

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