3. A car is travelling on a straight road. For 0 leq t leq 24 seconds, the car?s

Question

3. A car is travelling on a straight road. For 0 leq t leq 24 seconds, the car?s velocity v(t) in meters per second, is modeled by the piecewise-linear function defined by the graph above. (a) Find integral v(t) dt between the limits 0 and 24 . Using correct units, explain of Integrate v(t) dt between the limits 0 and 24 (b)for each of v?(4) and v?(20), find the value or explain why it does exist. Indicate units of measure. . (c) Let a(t) be the car's acceleration at time t, in meters per second per second. For 0

Explanation / Answer

a)

integration of v(t)*dt will be the area under the curve.

so now as it is a parallelogram,the area will be =0.5*((24-0)+(16-4))*20=360 m

so it represents the total distance travelled.

b) v'(4) does not exist, as the function v(t) is not continuous at t=4.

same applies for t=20

c)a(t)=dv/dt

so for 0<t<4, a(t)=(20/4)=5

for 4<t<16,a(t)=0

for 16<t<24, a(t)= (0-20)/(24-16)=-5/2=-2.5

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