Question

The sports car travels along a straight road such

that its acceleration is described by the graph. Construct the
v-s graph for the same interval and specify the velocity of
the car when s = 10 m and s = 15 m.

Answer 1

at s = 10m, v(t_1) = 7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Explanation:

for the interval 0-10 seconds,

a(t) = t m/s^2

v(0) = 0

v(t) = v(0) + integral(a(t)dt)

= 0 + [t^2/2]

= (1/2) t^2

s(0) = 0 .................. arbitrary

s(t) = s(0) + integral(v(t)dt)

= 0 + integral ((1/2)t^2)

= (1/6)t^3

When s(t) = 10 m,

(1/6)t^3 = 10

t^3 = 60

t_1 = 60 ^(1/3) = 3.9149 s approx.

v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s

When s = 15 m

(1/6)t^3 = 15

t^3 = 90

t_2 = 4.4814 s approx.

v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s