Question

1. a 1750-kg car accelerates east from rest to a speed of 25 m/s in 8.50 s.

a. calculate the acceleration of the car
b. calculate the net force needed to accelerate the car
c. calculate the amount of work done to accelerate the car
d. calculate the minimum power needed to accelerate the car
givens and unknowns
equations and constants

Explanation:

Step1: List given values

Mass $m = 1750\ \text{kg}$, initial velocity $v_0 = 0\ \text{m/s}$, final velocity $v = 25\ \text{m/s}$, time $t = 8.50\ \text{s}$

Step2: Calculate acceleration (part a)

Use $a=\frac{v-v_0}{t}$
$$a=\frac{25-0}{8.50}=\frac{25}{8.50}\approx2.94\ \text{m/s}^2$$

Step3: Calculate net force (part b)

Use $F=ma$
$$F=1750\times2.94\approx5145\ \text{N}$$

Step4: Calculate work done (part c)

Use work-kinetic energy theorem $W=\Delta KE=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2$
$$W=\frac{1}{2}\times1750\times25^2 - 0=\frac{1}{2}\times1750\times625=546875\ \text{J}$$

Step5: Calculate minimum power (part d)

Use $P=\frac{W}{t}$
$$P=\frac{546875}{8.50}\approx64338\ \text{W}$$

Answer:

a. $2.94\ \text{m/s}^2$ east
b. $5145\ \text{N}$ east
c. $5.47\times10^5\ \text{J}$
d. $6.43\times10^4\ \text{W}$