# Calculating distance when velocity is given

Mathematics Asked by Aruha on July 27, 2020

How to find the distance in $$0 < t < 2$$ when the velocity is given:

$$v(t) = frac{t^3}{10} – frac{t^2}{20} + 1$$

I have tried the following and got the answer as $$2.267$$

begin{align*} d = int_{0}^{2}v(t)mathrm{d}t & Longleftrightarrow d = int_{0}^{2} left(frac{t^{3}}{10} – frac{t^{2}}{20}+1right)mathrm{d}t\\ & Longleftrightarrow d = left(frac{t^{4}}{40} – frac{t^{3}}{60}+tright)Big|_{0}^{2}\\ & Longleftrightarrow d = 2.267 m end{align*}
Is this approach correct? Kindly help.

There is a distinction between the difference of the particle's position between the instants $$t_{2} > t_{1}$$ and the distance traveled by the particle corresponding to the time interval $$Delta t = t_{2} -t_{1}$$. The first is given by the integral of $$v(t)$$ and the second is given by the integral of $$|v(t)|$$. Depending in which case you are interested, you can calculate the corresponding integral in order to obtain the answer.

Answered by user1337 on July 27, 2020

## Related Questions

### If $A$ is a matrix such that $A^T = A^2$, what are eigenvalues of $A$?

2  Asked on December 15, 2021

### Triangles and a square

0  Asked on December 15, 2021

### Galiliean group vs Poincare group and role of mass

1  Asked on December 15, 2021

### Solve for x, such that: $sum_{n=0} frac{x}{4^n} = sum_{n=0} frac{1}{x^n}$

3  Asked on December 15, 2021 by b-c

### A quick way to tell local minimum given a sum of absolute value functions

1  Asked on December 15, 2021

### Integral from normal variable.

0  Asked on December 15, 2021 by captain-nick

### What is the order and structure of Aut(SL$_2(p)$)?

1  Asked on December 15, 2021 by david-popovi

### subsection ‘Difference equation’ in Strang’s linear algebra section 6.3

1  Asked on December 15, 2021 by oscarmetal-break

### Proof of the error function being holomorphic and independent of path

0  Asked on December 15, 2021 by korgboll

### How can I prove $A − A(A + B)^{−1}A = B − B(A + B)^{−1}B$ for matrices $A$ and $B$?

2  Asked on December 15, 2021

### How does the author derive these relations?

1  Asked on December 15, 2021

### Prove two equation about $H_{p} (X)$ and $kernel (i_{n_{*}})_{p}$ .

2  Asked on December 15, 2021

### If $B$ is a $C^*$-subalgebra of $A$, then $sigma_A(b) cup {0} = sigma_B(b) cup {0}$

0  Asked on December 15, 2021

### Determinantal/Fitting ideal of the direct sum of linear maps

0  Asked on December 15, 2021

### Condition on ratio related to bipartite graph

0  Asked on December 15, 2021 by chao

### Proof for a combinatorial identity

2  Asked on December 15, 2021

### What is the probability space of typical real univariate probability distributions?

5  Asked on December 15, 2021 by lars-ericson

### Reusing samples from a probability distribution

0  Asked on December 15, 2021

### Proof Check: Multiplication operator on $L^{p}(mathbb R^{d})$ is closed

0  Asked on December 15, 2021

### Prove that in a triangle $sumlimits_{cyc}frac{w_bw_c}{w_a}geqfrac{3}{4}left(sumlimits_{cyc}frac{a^2w_a}{w_bw_c}right)geqsqrt{3}s$

1  Asked on December 15, 2021

### Ask a Question

Get help from others!