Question

A particle moves in a circle of radius 2.0 cm at a speed given by v = 4t, where v is in cm/s and t is in seconds.
Find the tangential acceleration at t =1 s.
Find total acceleration at t =1 s.

• A. Tangential acceleration $=2cm/s^2$
  Total acceleration $=4\sqrt{5}cm/s^2$
• B. Tangential acceleration $=4cm/s^2$
  Radial acceleration $=4\sqrt{5}cm/s^2$
• C. Tangential acceleration $=2cm/s^2$
  Radial acceleration $=8cm/s^2$
• D. Tangential acceleration $=4cm/s^2$
  Radial acceleration $=16cm/s^2$

Answer 1

The correct option is B

Tangential acceleration $=4cm/s^2$
Radial acceleration $=4\sqrt{5}cm/s^2$

Tangential acceleration, $a_t=\frac{dv}{dt}=\frac{d}{dt}\left(4t\right)=4cm/s^2$
Radial acceleration, $a_r=\frac{v^2}{R}=\frac{(4{)}^2}{2}=8cm/s^2$
Hence, total acceleration, $a=\sqrt{a_t^2+a_r^2}=4\sqrt{5}cm/s^2$