## Related questions with answers

A particle moves with acceleration a(t) m/

$s^2$

along and s-axis and has velocity

$v_0$

m/s at time t=0. FInd the displacement and the distance traveled by the particle during the given time interval. a(t)=-2;

$v_0$

=3;

$1 \leq t \leq 4$

Solutions

VerifiedIn this problem, we have to determine the distance traveled by the moving object and the displacement with an acceleration function $a(t)=-2$ over the time interval $[1,4]$ and at time $0$ its velocity is $3$.

Recall the formula for velocity:

$\color{#c34632} v(t)=\int a(t)\ d t \qquad (1)$

And the formula for displacement over the time interval $\left[t_{0}, t_{1}\right]$:

$\color{#c34632} \int_{t_{0}}^{t_{1}} v(t) d t=\int_{t_{0}}^{t_{1}} s^{\prime}(t) d t=s\left(t_{1}\right)-s\left(t_{0}\right)\qquad (2)$

Also, the formula for distance traveled during time interval $\left[t_{0}, t_{1}\right]$:

$\color{#c34632} \int_{t_{0}}^{t_{1}}|v(t)| d t \qquad (3)$

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