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

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

Tardigrade Admin · Accepted Answer

v = 2t, ac = (ν2/r) = ((2t)2/0.2) = 20t2 = 20 × 22 = 80 m/s2 at = (dv/dt) = 2 m/s2 Net acceleration: a = √a2c + at2 > 80 m/s2

Q. 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

the radial acceleration at $t = 2 s i s 80 m s^{- 2}$

tangential acceleration at $t = 2 s i s 2 m s^{- 1}$

net acceleration at t = 2 s is greater than 80 $m s^{- 1}$

tangential acceleration remains constant in magnitude

v = 2t, $a_{c} = \frac{ν ^{2}}{r} = \frac{( 2 t ) ^{2}}{0.2}$ = 20t $^{2}$ = 20 $\times 2^{2}$ = 80 m/s $^{2}$
$a_{t} = \frac{d v}{d t}$ = 2 m/s $^{2}$
Net acceleration : a = $a_{c}^{2} + a_{t}^{2}$ > 80 m/s $^{2}$

Q. 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

the radial acceleration at t=2sis80ms−2

tangential acceleration at t=2sis2ms−1

net acceleration at t = 2 s is greater than 80 ms−1

tangential acceleration remains constant in magnitude

v = 2t, ac​=rν2​=0.2(2t)2​ = 20t2 = 20 ×22 = 80 m/s2 at​=dtdv​ = 2 m/s2 Net acceleration : a = ac2​+at2​​ > 80 m/s2

the radial acceleration at $t = 2 s i s 80 m s^{- 2}$

tangential acceleration at $t = 2 s i s 2 m s^{- 1}$

net acceleration at t = 2 s is greater than 80 $m s^{- 1}$

v = 2t, $a_{c} = \frac{ν ^{2}}{r} = \frac{( 2 t ) ^{2}}{0.2}$ = 20t $^{2}$ = 20 $\times 2^{2}$ = 80 m/s $^{2}$
$a_{t} = \frac{d v}{d t}$ = 2 m/s $^{2}$
Net acceleration : a = $a_{c}^{2} + a_{t}^{2}$ > 80 m/s $^{2}$