Question

What constant acceleration in si units must a car have to go from zero to 60 mph in 10s. what fraction of g is this?

Answer 1

The acceleration of the car in SI units is 2.68m/s².

The acceleration is 0.27 times the acceleration due to gravity g.

Convert the speed in mph into m/s.

1 mile = 1609 m and 1h = 3600 s.

Therefore,

$v=(\frac{60 miles}{1 h} )(\frac{1609 m}{1 mile} )(\frac{1h}{3600s)} =26.82m/s$

Acceleration is the rate of change of velocity. The car starts from rest , its initial velocity u = 0 and accelerates to a velocity v of 26.82 m/s in 10 s.

Use these values in the equation and calculate the acceleration.

$a=\frac{v-u}{t} \\ =\frac{(26.82 m/s)-(0m/s)}{10s} \\ =2.682 m/s^2$

Thus the car accelerates at a rate of 2.68 m/s².

The acceleration due to gravity g on Earth has a value 9.81 m/s².

Find the ratio$\frac{a}{g}$

$\frac{a}{g} =\frac{2.682m/s^2}{9.81m/s^2} \\ =0.27 a=0.27g$

The car's acceleration is 0.27 times the value of g.