Velocity and Acceleration Calculator

Ask and get solution to your homeworkAsk now and get step-by-step solutions

Example

Created on 2024-06-20Asked by Camila Miller (Solvelet student)

A particle moves along a straight line with velocity

v(t) = 3t^2 + 2t

m/s. Find the acceleration function

a(t)

Solution

Given that the velocity function

v(t) = 3t^2 + 2t

m/s, we need to find the acceleration function

a(t)

. To find

a(t)

, we differentiate the velocity function with respect to time

t

a(t) = \frac{dv}{dt} = \frac{d}{dt}(3t^2 + 2t).

Differentiating each term separately, we get:

\frac{d}{dt}(3t^2) + \frac{d}{dt}(2t).

Using the power rule of differentiation, we have:

a(t) = 6t + 2.

Therefore, the acceleration function

a(t)

6t + 2

m/s

^2

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Oliver White on Solvelet

1. Given the position function

s(t)=3t^2-2t+5

, find the velocity and acceleration functions.2. A particle moves along the x-axis according to the position function

x(t) = 2t^3 - 6t^2 + 4t - 1

. Find the time when the particle's velocity is zero.,

DefinitionThe rate of change of position with respect to time is defined as velocity & rate at which velocity is changing with respect to time is called acceleration. Both are vector quantities. ex: s(t)=t2 => v(t)=2t => a(t)=2, for an object.

Related Calculators

Matrix Inversion Calculator Graph Theory Calculator Tabular integration Calculator Rates and Ratios Calculator

Need topic explanation ? Get video explanation