Question

1. A racing car starts from rest and reaches a final speed v in a time interval of t after traveling a distance on a straight line. If the acceleration a of the car is constant during this time, which of the following statements can not be true? (a) The car travels a distance of v 2 2a . (b) The acceleration of the car is v 2t 2 . (c) The velocity of the car at t/2 (at one half of the time interval t) is 1 2 at2 .

A) Statement (a) only

B) Statement (b) only

C) Statement (c) only

D) Statements (b) and (c)

Answer 1

U = initial speed of car = 0 m/sec

V = final speed of car after time 't' = v

a = acceleration of car

Now Using 1st kinematic equation:

V = U + a*t

v = 0 + a*t

a = v/t

Using 2nd kinematic equation:

d = U*t + (1/2)*a*t^2

d = 0*t + (1/2)*a*t^2

Since a = v/t, Since t = v/a

d = (1/2)*a*(v/a)^2 = v^2/(2*a)

Again using 1st kinematic equation when t = t/2

V = U + a*t

v1 = 0 + (v/t)*(t/2) = v/2

Please check your options and match the answers, as options are not clearly mentioned here, If you've any query let me know in comment section.