Linear motion Calculator

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Example

Created on 2024-06-20Asked by Alexander Walker (Solvelet student)

A car accelerates uniformly from rest and reaches a speed of 30 m/s in 10 seconds. Find the acceleration and the distance traveled in this time.

Solution

To find the acceleration and the distance traveled by the car, we use the equations of linear motion. Given:

u = 0 \, \text{m/s} \quad (\text{initial velocity})

v = 30 \, \text{m/s} \quad (\text{final velocity})

t = 10 \, \text{s} \quad (\text{time})

First, we find the acceleration using the equation:

v = u + at

30 = 0 + a \cdot 10

a = \frac{30}{10} = 3 \, \text{m/s}^2

Next, we find the distance traveled using the equation:

s = ut + \frac{1}{2}at^2

s = 0 \cdot 10 + \frac{1}{2} \cdot 3 \cdot 10^2

s = \frac{1}{2} \cdot 3 \cdot 100 = 150 \, \text{m}

Therefore, the acceleration is

3 \, \text{m/s}^2

and the distance traveled is

150 \, \text{m}

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Some of the related questions asked by Lucas Walker on Solvelet

1. Calculate the displacement of an object that moves 5 meters north and then 3 meters south.2. Find the final velocity of a car that accelerates uniformly from rest to 20 m/s in 10 seconds

DefinitionLinear motion is the motion of a body along a straight path. Basic parameters include the displacement, velocity, and acceleration. According to the latter, linear motion can be uniform or non-uniform. If an object travels a straight line with a 10 m distance at a speed of 5 m/s, it is an example of linear motion. Linear programming is a technique for solving optimization problems in which the dependent variable is modeled as a linear objective functional of the optimized variables. Constraints, taken together, can be represented in the form of a convex feasible region. An example of a linear differential equation is. Linear transformations operate vector spaces, and the result is also another vector space. The example of a linear transformation is a map given by matrices or differential operators.

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