Question

A car starts from rest and has an acceleration a = t. A truck is moving with a uniform velocity of6 m/s. At what distance will the car overtake the truck? (at t= 0 both start their motion in thesame direction from the same position)

Answer 1

Final Answer :
$\red {t = 6s}$

Steps:
1) Observing the question, we get
Initially Truck will be ahead of car due to constant speed 6 m/s .
=>Slowly, and Gradually due to accelerated car with time, it will get ahead of truck at some time.

=>At that time, displacement of both vehicles will be same.

2) Displacement of Truck in time t :
=>Constant velocity * Time
$s _{truck} = 6t \: m$


3) Velocity of car at time t :
initial t = 0 , initial v = 0
$v = \int_ {0}^{t} t \: dt \: = \frac{ {t}^{2} }{2}$
Displacement at time t :
$s _{car}= \int_{0}^{t} \frac{ {t}^{2} }{2} \: dt = \frac{ {t}^{3} }{6}$

4) Then, we have
$s _{car} = s _{truck} \\ = > \frac{ {t}^{3} }{6} = 6t \\ = > {t}^{2} = 36 \: \:as \: (t \: \neq \: 0) \\ = > t = 6 \: \: \: as \: (t \: is \: + ve)$
Hence, Required Time is at t= 6s.

Answer 2

Answer:

36m

Explanation:

the above explanation is completely correct but the final answer is 36m bcuz they haven't asked time, they have asked distance at which car will overtake the truck