Question

The combined mass of a race car and its driver is 600 kg. Travelling at constant speed, the car completes one lap around a circular track of radius 160 m in a total time of 36 s. What is the magnitude of the centripetal acceleration of the car? (π = 3.142)

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Centripetal\:acceleration=2.5\:m/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Mass \: of \: car(m)= 600 \: kg \\ \\ \tt: \implies Radius \: of \: circular \: track(r)= 160 \: m \\ \\ \tt: \implies Time(t) = 36 \: sec \\ \\ \red{\underline \bold{To \: find:}} \\ \tt :\implies Centripetal \: acceleration( a _{c}) =?$

• According to given question :

$\tt \circ \: Acceleration = 0 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies s = ut + \frac{1}{2} {at}^{2} \\ \\ \tt: \implies 2\pi r = u \times 36 + \frac{1}{2} \times 0 \times {36}^{2} \\ \\ \tt: \implies \frac{2\pi \times 160}{36} = u \\ \\ \green{\tt: \implies u = \frac{320\pi}{36} =v} \\ \\ \bold{For \: centripetal \: acceleration :} \\ \tt: \implies a_{c} = \frac{ {v}^{2} }{r} \\ \\ \tt: \implies a_{c} = \frac{ (\frac{320\pi}{36})^{2} }{320} \\ \\ \tt: \implies a_{c} = \frac{320 \times 320 \times {\pi}^{2} }{ {36}^{2} \times 320} \\\\ \tt\circ\:\pi^{2}=10\\ \\ \tt: \implies a_{c} = \frac{320 \times 10}{1296} \\ \\ \tt: \implies a_{c} = \frac{3200}{1296} \\ \\ \green{\tt: \implies a_{c} =2.5 \: m/{s}^{2} } \\ \\ \green{\tt \therefore Centripetal \: acceleration \: is \: 2.5 \: m/{s}^{2} }$