# Car along curved path

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A car travels along the curved path with radius of curvature p= 30m such that its speed is increased by v= (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.

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Since v(t)=v0*e^t where v0=0.5 m/s we have

s(t1)-s(0)= integral of v(t)dt from t=0 to t=t1 (the time at which s=18 m), this gives (in standard units):

s(t1)=18=v0(e^t1-1)

substituting 0.5 for v0 we can find ...

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