Question

a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s? b. How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

Short answer

(a) The constant acceleration of a car is $2.7\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$.

(b) The distance traveled by car isrole="math" localid="1648062211916" $133m$(SI units) androle="math" localid="1648062258709" $436ft$(in feet).

Step-by-step solution

Given information

The initial velocity of a car is $v_{is}=0mph$.

The final velocity of a car is role="math" localid="1648060853938" $v_{fs}=60mph$.

Time role="math" localid="1648061198818" $∆t=10s$

Part (a): Find the constant acceleration in SI units.

As we need to find the answer in SI units, convert velocity in mph to $\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.

$1mph=0.447\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

$v_{fs}=60\times 0.447=26.82\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Use kinematical equation, $v_{fs}=v_{is}+a∆t$

Substitute the known values,

$$\begin{gathered} 26.82=0+a\left(10\right) \\ a=\frac{26.82}{10} \\ =2.68 \\ \approx 2.7\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right. \end{gathered}$$

Therefore, the constant acceleration of a car in SI units is$2.7\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$.

Part (b): Find the distance traveled by car in SI units and in feet.

Use kinematical equation, ${v^2}_{fs}={v^2}_{is}+2a_s∆s$.

Substitute the known values,

localid="1648061677839" $$\begin{gathered} 26.{82}^2=0+2\left(2.7\right)∆s \\ 719.31=5.4∆s \\ ∆s=\frac{719.31}{5.4} \\ \approx 133m \end{gathered}$$

Convert the obtained answer in SI units to feet.

localid="1648062335788" $1m=3.28ft$

localid="1648062347256" $$\begin{gathered} 133m=133\times 3.28 \\ \approx 436ft \end{gathered}$$

Therefore, the distance traveled by car in SI units is $133m$and in feet is

436 ft. .