Generally, we consider that during slowing of a moving automobile, its retardation is constant, but in practice this is seldom the case. Under many circumstances, especially at high speed, we usually apply the brakes slowly at first and then more strongly as the car slows. The braking force therefore depends on the time during the interval over which the car is slowing and acceleration changes with time.
`a_(x)(t)=(v_(A)-v_(x))/(dt) =(F_(x)(t))/(m)`
`int_(v_(0_(x)))^(v_(x))dV_(x)=int_(0)^(1)(F_(x)(t))/(m)dt`
`therefore V_(x)=V_(0x)+(1)/(m) int_(0)^(1)F_(x) (t) dt`
`x(t)=x_(0)+int_(0)^(1) V_(x) (t) dt `
An example for the same is discussed here.
A car of mass m = 1000 kg is moving with 25 m/s. The driver begins to apply the brakes so that the magnitude of the braking force increases linearly with time at a rate of 2000 N/s.
Read the above passage carefully and answer the following questions.
How much time passes before the car comes to rest?

Options

A. 5 sec
B. 4 sec
C. 8 sec
D. 6.5 sec

Answer

A