[فيزيائي 2009]

Motion along a straight line - problem 2

A car accelerates from a standstill to 100 km/h in 12 s. Assuming constant acceleration, what is the distance it travels during that time?

We denote the quantities given in this problem as follows:

time of travel t=12 s, final speed vf = 100 km/h.

We are looking for the total distance x traveled during this time t.

We will classify this as a

motion along a straight line, with initial velocity v0=0, and initial distance traveled x0=0.

Equation M1.30 from this chapter

but with v0=0 and x0=0 it is

x = at2 / 2 [1]

The only unknown quantity in this equation is acceleration a.

In motion with constant acceleration we can use Eq. M1.11, from this chapter, which has the form

but we do not have to use vector notation, as we are not considering the direction of this motion.

Dt from this equation is the time t form this problem – the time during which the speed changed.

Dv is the total change of speed that is the final v in our problem. With the notation given above

a = v / t

and after substituting this to Eq. [1], the distance traveled is

x=(1/2)*(v / t)* t2 = (1/2) v * t [2]

The dimension for this answer is

[x] = (km / h) * h = km

which is correct, distance must be in units of length.

After substituting numerical values to the solution given by Eq. 2 we get

x=(1/2) *100 * (12/3600) = 0.1667 km

We write 12/3600 to change time given in seconds into hours.