Question

the velocity of a car moving on a straight road increase linearly according to equation V is equal to a + bx where a and b are constant the acceleration in the course of such motion

Answer 1

The velocity of a car moving on a straight road increase linearly according to equation, v = a + bx

where a and b are constants.

differentiating both sides with respect to time,

i.e., dv/dt = d(a + bx)/dt

= 0 + b × dx/dt

we get, dv/dt = b (dx/dt) .....(1)

we know, acceleration is the rate of change of velocity with respect to time.

so, a = ∆v/∆t

for instantaneous acceleration, a = dv/dt....(2)

and displacement is the rate of change of velocity with respect to time.

i.e., v = dx/dt ....(3)

from equations (1), (2) and (3),

a = bv

putting v = a + bx

so acceleration , a = b(a + bx) = ab + b²x

hence, required answer is, a = ab + b²x.