physic for scientists and engineers




physics for scientists and engineers?

A car stats from rest and accelerates uniformly for 6 s.
The distance traveled in the 6 s is greater than the distance traveled in the first second by what factor?

Distance traveled under constant acceleration:
d = 1/2*a*t^2 + v0*t + d0

d0 = 0 because I said so
v0 = 0 because it begins at rest

thus
d = 1/2*a*t^2

For time interval 1:
d1 = 1/2*a*t1^2

For the total time:
d_net = 1/2*a*t_net^2

We are interested in the value of d_net/d1:
d_net/d1 = (1/2*a*t_net^2)/(1/2*a*t1^2)

Simplify:
d_net/d1 = t_net^2/t1^2

Data:
t_net:=6 seconds; t1:=1 second;

Result:
d_net/d1 = 36

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