Chapter 3, Problem 96A

To determine

The time taken by the truck to catch up the car. Also, the meeting point of car and truck.

Answer to Problem 96A

After 12 sec trave/lling a distance of 180 m both truck and car will meet.

Explanation of Solution

Given:

Acceleration of the truck $a=2.5{\text{ m/sec}}^2$

Speed of the car $u=15\text{ m/sec}$

Formula used:

Distance travelled by an object, if it is moving with a speed s in time t is,

  $s=vt$

Also, according to equation of motion, distance travelled by an object is

  $s=ut+\frac{1}{2}a{t}^2$

Where,

a is the acceleration of an object

u is the initial velocity

t is the time taken.

Calculation:

It is given that initially truck is stopped.

Therefore, initial velocity of truck is $u=0\text{ m/sec}$

Let after t sec both car and truck meet.

Distance travelled by car in t sec.

  $\begin{array}{c}s=ut\\ =15t\text{ m}\end{array}$  (1)

Distance travelled by truck in t sec is

  $\begin{array}{c}s=ut+\frac{1}{2}a{t}^2\\ =0\times t+\frac{1}{2}\times 2.5\times t^2\\ =1.25t^2\text{ m}\end{array}$  (2)

When both car and truck met, then distance travelled by both is same.

Therefore, from equation (1) and (2).

  $\begin{array}{l}1.25t^2=15t\\ 1.25t^2-15t=0\\ t\left(1.25t-15\right)=0\\ t=0\text{ s},t=12\text{ s}\end{array}$

As t = 0 sec is not possible so truck and car will meet after 12 sec.

Now distance travelled by truck and car in 12 sec.

  $\begin{array}{c}s=15t\\ =15\times 12\\ =180\text{ m}\end{array}$

Conclusion:

Therefore, after 12 sec travelling a distance of 180 m both truck and car will meet.