Question

a car starts from rest and reaches a speed 8km/s in 2sec and then moves with the same speed for another 3sec .The total distance travelled by the car in 5 sec is
(a) 8m
(b) 16m
(c)24m
(d) 32m

pls give correct answer vth detalied explanation​

Answer 1

Correct Question :-

A car starts from rest and reaches a speed 8 ms⁻¹ in 2 sec and then moves with the same speed for another 3 sec. The total distance traveled by the Car in 5 sec is

(a) 8 m

(b) 16 m

(c) 24 m

(d) 32 m

Given :-

• initial velocity of Car , u = 0
• final velocity of Car , v = 8 ms⁻¹
• time taken for change in velocity = 2 s
• Car after attaining velocity 8 ms⁻¹ moves with the same speed for 3 sec

To find :-

• Total distance covered by Car in 5 sec

Formula required :-

• First equation of motion

$\gray{\bigstar}\boxed{\sf{v=u+at}}$

• second equation of motion

$\gray{\bigstar}\boxed{\sf{s=ut+\dfrac{1}{2}at^2}}$

(where u = initial velocity ; v = final velocity ; a = acceleration ; t = time taken ; s = distance covered)

Solution :-

▶Calculating Distance covered by Car for attaining a velocity of 8 ms⁻¹

initial velocity , u₁  = 0

final velocity ,v₁ = 8 ms⁻¹

time for attaining final velocity, t₁ = 2 sec

Let, acceleration of Car = a₁

and distance traveled by Car = s₁

Using first equation of motion

$\longmapsto \sf{v_1=u_1+a_1t_1}\\\\\longmapsto\sf{8=0+a_1(2)}\\\\\longmapsto\underline{\underline{\large{\purple{\sf{a_1=4\;\;ms^{-2}}}}}}$

Using second equation of motion

$\longmapsto\sf{s_1=u_1t_1+\dfrac{1}{2}a_1{t_1}^2}\\\\\longmapsto\sf{s_1=(0)(2)+\dfrac{1}{2}(4)(2)^2}\\\\\longmapsto\underline{\underline{\large{\purple{\sf{s_1=8\;\;m}}}}}$

▶ Calculating distance covered by Car while moving with a constant speed 8 ms⁻¹ for 3 sec

since , Car is moving with constant velocity

hence,

acceleration of car , a₂ = 0

initial velocity , u₂ = 8 ms⁻¹

final velocity of Car , v₂ = 8 ms⁻¹

time for which Car moved, t₂ = 3 sec

distance traveled by Car = s₂

Using second equation of motion

$\longmapsto\sf{s_2=u_2t_2+\dfrac{1}{2}a_2{t_2}^2}\\\\\longmapsto\sf{s_2=(8)(3)+\dfrac{1}{2}(0)(3)^2}\\\\\longmapsto\underline{\underline{\large{\purple{\sf{s_2=24\;\;m}}}}}$

▶ Calculating total distance covered by Car

$\longmapsto\sf{total\:distance\:covered\:by\:car=s_1+s_2}\\\\\longmapsto\sf{total\:distance\:covered\:by\:Car=8+24}\\\\\longmapsto\underline{\boxed{\large{\pink{\sf{total\:distance\:traveled\:by\:Car=32\;\;m}}}}}$

Hence,

Option (d) 32 m is Correct .