Answer to Question #149056 in Physics for Melanie Belandres

Question

4. A triumph TR-7 starts at rest and accelerates to a speed of 27 m/s in 11.8 s. (a) Calculate the car’s acceleration. (b) Calculate the distance traveled during this time.

Answer 1

(a) We can find the car's acceleration from the kinematic equation:

$$v=v_0+at,$$ $$a=\dfrac{v-v_0}{t}=\dfrac{27\ \dfrac{m}{s}-0\ \dfrac{m}{s}}{11.8\ s}=2.28\ \dfrac{m}{s^2}.$$

(b) We can find the distance traveled during this time from the kinematic eqquation:

$$d=v_0t+\dfrac{1}{2}at^2,$$ $$d=\dfrac{1}{2}\cdot 2.28\ \dfrac{m}{s^2}\cdot (11.8\ s)^2=159\ m.$$

Answer:

(a) $a=2.28\ \dfrac{m}{s^2}.$

(b) $d=159\ m.$