Question

A particle moves in a circle of radius 20 cm. Its linear speed is given by v = 2t . where t is in s and v in m/s. Then

• A. the radial acceleration at $ t = 2s is 80ms^{-2}$
• B. tangential acceleration at $t = 2s is 2 ms^{-1}$
• C. net acceleration at t = 2 s is greater than 80 $ms^{-1}$
• D. tangential acceleration remains constant in magnitude

Answer 1

Answer: (D)

v = 2t, $a_c = \frac{\nu^2}{r} = \frac{(2t)^2}{0.2}$ = 20t$^2$ = 20 $\times 2^2$ = 80 m/s$^2$
$a_t = \frac{dv}{dt} $ = 2 m/s$^2$
Net acceleration : a = $\sqrt{a^2_c + a_t^2} $ > 80 m/s$^2$