Acar accelerates from rest with an acceleration of 5 m/s^2. the acceleration decreases linearly with time to zero in 15 s, after which the car continues with constant speed. at what time t will the car have moved 500 m from its starting point?

At time 18.33 seconds it will have moved 500 meters.

Explanation:

Since the acceleration of the car is a linear function of time it can be written as a function of time as

Integrating both sides we get

Now since car starts from rest thus at time t = 0 ; v=0 thus c=0

again integrating with respect to time we get

Now let us assume that car starts from origin thus D=0

thus in the first 15 seconds it covers a distance of

Thus the remaining 125 meters will be covered with a constant speed of

in time equalling

Thus the total time it requires equals 15+3.33 seconds

t=18.33 seconds

yes indeed

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