Question

The instantaneous speed of a particle moving along one straight line is v(t) = ate−4t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

Answer: V= a

Answer 1

$v=ate^{-4t}$

$\frac {dv}{dt}=a(1-4t)e^{-4t}=0$ (For maximum)

$t=\frac {1}{4}$

$v_{max}=a\frac {1}{4}e^{-4\cdot \frac {1}{4}}=0.09196\ a$