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Question

A car starts from rest and acceleration at $$4\ {m/s}^{2}$$ for $$5\ s$$. After that it moves with constant velocity for $$25\ s$$ and then retards at $$2\ m/s^{2}$$ until it comes to rest. The total distance travelled by the car is


A
650 m
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B
527 m
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C
675 m
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D
573 m
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Solution

The correct option is A $$650\ m$$
For $$0-5 sec$$, 
$$a= 4m/s^2$$, Let velocity at $$ 5 sec$$ is $$v$$ and distance is $$S_1$$
Using $$v=u+at$$   $$\Rightarrow v= 0+4\times 5=20 m/s$$
Using $$s= ut+\dfrac{1}{2}at^2$$  $$\Rightarrow  S_1=0+\dfrac{1}{2}\times 4\times 5^2=50m$$
For next $$25sec$$
$$v= 20 m/s$$  
$$\Rightarrow S_2= 20\times 25= 500 m$$
For comes to rest, 
$$u= 20 m/s $$ , $$a=-2 m/s^2$$ 
Using $$v^2=u^2+2as$$   $$\Rightarrow 0=20^2-2\times 2\times S_3$$
$$\Rightarrow S_3= 100 m$$
Total distance $$= S_1+S_2+S_3= 50+500+100=650 m$$

Physics

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