A car travels along the curved path with radius of curvature p= 30m such that its speed is increased by at = (0.5e^t) m/s^2, where t is in seconds. determine the magnitudes of its velocity and acceleration after the car has traveled s = 18m starting from rest. neglect the size of the car.

Answer 1

The distance s travelled in time t' is
S (t') = Double integral a_t dt
t=0 to t'
18 = 0.5*e^t' meters
t' = ln 36 = 3.584 s

V (t') = Single integral a_t dt
t=0 to t'
= 0.5*e^t' = 18 m/s

a_t (t') = 18 m/s^2

There is also a centrifugal acceleration component,
a_r = V(t')^2/R = 324/30 = 10.8 m/s^2

Answer 2

you're a lifesaver
thank you!

Answer 3

Above answer is completely wrong.. it seems he forgot that it's an initial value problem