How Do You Calculate Time and Distance for Deceleration in Physics?

[Mobz]

Homework Statement

A particle moving along a straight line decelerates according to a= -kv, where k is a constant and v is velocity. If its initial velocity at time t=0 iv v0=4 m/s and its velocity at time t=2 s is v = 1 m/s, determine the time T and corresponding distance D for the particle speed to be reduced to one-tenth of its initial value

ans T = 3.32 s, D = 5.19 M

Homework Equations

The Attempt at a Solution

I have never tried a problem like this.. I just need some instruction on how to start.

Thanks you very much!

 

[LowlyPion]

Homework Statement

A particle moving along a straight line decelerates according to a= -kv, where k is a constant and v is velocity. If its initial velocity at time t=0 iv v0=4 m/s and its velocity at time t=2 s is v = 1 m/s, determine the time T and corresponding distance D for the particle speed to be reduced to one-tenth of its initial value

ans T = 3.32 s, D = 5.19 M

Homework Equations

The Attempt at a Solution

I have never tried a problem like this.. I just need some instruction on how to start.

Thanks you very much!

Welcome to PF.

Notice first your equation a = -kv expresses Acceleration as a variable in V.
Hence to develop an equation expressing V as a function of t you will need to integrate a which is dv/dt. Rearranging your equation you have then:

1/v*dv = -k*dt

Integrating you get something of the form:

ln|v| = -k*t + c

You can use the values given to determine the constants of the equation.