Question

A particle moves in a circle of radius 1.0 cm at a speed given by v=2t, where v is in cm/s and t in seconds. Find the tangential acceleration at t=1s.

Answer 1

Hint: The rate of change of an object's velocity with respect to time is called acceleration in mechanics. Accelerations are quantities that are measured in vectors (in that they have magnitude and direction). The orientation of the net force acting on an object determines the orientation of its acceleration.

Formula used:
${a_t} = \dfrac{{\Delta v}}{{\Delta t}}$
$\Delta v$= change in velocity
$\Delta t$= change in time

Complete step-by-step answer:
According to Newton's Second Law, the magnitude of an object's acceleration is the product of two factors: the total balance of all external forces operating on the object — magnitude is directly proportional to this net resultant power.
the object's density, which varies depending on the materials used in its construction — magnitude is inversely proportional to mass.
The metre per second squared is the SI unit for acceleration.
Tangential acceleration is a term that is used to quantify the difference in tangential velocity of a point with a given radius as time passes. The linear and tangential accelerations are the same, but the circular motion is caused by the tangential acceleration. The rate of change of the tangential velocity of the matter in a circular direction is known as tangential acceleration.
Tangential acceleration and related parameters are calculated using the tangential acceleration formula, with $m{s^{ - 2}}$ as the unit.
Given the velocity of the particle, $\Delta v = $2t
$\Delta t = $1 s
${{\text{a}}_{\text{t}}} = \dfrac{{{\text{d}}[{\text{v}}({\text{t}})]}}{{{\text{dt}}}} = \dfrac{{{\text{d}}(2{\text{t}})}}{{{\text{dt}}}} = 2\;{\text{cm}}/{{\text{s}}^2}$
$ \Rightarrow {{\text{a}}_{\text{t}}} = 2\;{\text{cm}}/{{\text{s}}^2}$

Note: A particle encounters an acceleration due to a shift in the direction of the velocity vector while its magnitude stays constant in uniform circular motion, and is travelling at a constant speed along a circular path. The derivative of a point on a curve's position with respect to time, i.e. its velocity, is always exactly tangential to the curve, or orthogonal to the radius in this point.