Question

A car is initially at rest on a straight road. The histogram below shows the car's acceleration along that road as a function of time.

Link to histogram https://s4.lite.msu.edu/cgi-bin/plot.png?file=modykrun_msu_1400092982_11970255_plot.data

1) Calculate the speed of the car at t = 4 s.

2) Calculate the distance traveled during the first 5 s.

3) Calculate the distance traveled from t=10 s to t=13 s.

4) Calculatethe car's average speed from t = 5 s to t=9 s.

Answer 1

first you have to make the speed graph
0-1 s the speed is 0
1-3 s the speed increases form 0 to( 2*(3-1)^2)/2=4m/s
then it decreases from 4 m//s to 4-(1*(4-3)^2)/2=3.5 ms
Then it increases again ti 4 m/s (at 5 s) and it stays there intil the end.
All you need to do is calculate the area under the grapg and tivide it by 7s:

we have a triangle: 4m/s*2s/2=4m (1-3s)
two trapezoids: (3-4s 4-5s)
1s*(4m/s+3.5m/s)/2=3.75m
and a rectangle: (5-7s)
4m/s*2s=8m

Total "area" is: 4+3.75+3.75+8=19.5m
divided by 7s:

19.5/7=2.78m/s average