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Physics
30.05.2020 08:23
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A toy car is given an initial velocity of 5.0 m/s and experiences a constant acceleration

A toy car is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 2.0 m/s2. What is the final velocity after the 6.0 s?
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pr47723
pr47723
4,5(63 marks)

t=3.64s

Step by step explanation

Step 1

In this step we use the definition of acceleration to determine the expression to integrate. Note that the acceleration is the derivative of velocity with respect to time.

a=\frac{dv}{dt} \\\implies adt=dv\\\implies dv=(32t^3-11t^4)dt

Step 2

Perform  integration on the expression from step 1. This calculation is performed as shown below.

v=\int(32t^3-11t^4)dt\\v=\frac{32}{4}t^4- \frac{11}{5}t^5 +c\\\8t^4- \frac{11}{5}t^5 +c

Step 3

In this step we use the condition that at t=0, the velocity v=0 to find the exact form of the velocity function. We substitute  this point into the velocity function we found in step 2.

0=8(0)^4-\frac{11}{5} (0)^5+c\\\implies c=0

Step 4

We now  use the function in step 3  to find out when the velocity is zero again.

v=0=8t^5-\frac{11}{5}t^4\\\implies 0=8t^4-\frac{11}{5} t^5\\\implies t^4(8-\frac{11}{5} t)\\\implies t=0, 8-\frac{11}{5}t=0\\\\\implies t=0,t=\frac{40}{11} =3.64

The velocity is zero again when t=3.64

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