Question

An automobile with an initial speed of 4.47m/s accelerates uniformly at the rate of 3.0
m/s.

Answer 1

Answer on Question #46958-Physics-Mechanics-Kinematics-Dynamics

An automobile with an initial speed of $4.47\frac{\mathrm{m}}{\mathrm{s}}$ accelerates uniformly at the rate of $3.0\frac{\mathrm{m}}{\mathrm{s}^2}$. Find the final speed and the displacement after 5.0 s.

Solution

So first we solve for the displacement. We used this formula.

$$\Delta x = v_{i} \Delta t + \frac{1}{2} a \Delta t^{2},$$

where: $v_{i} = 4.47\frac{\mathrm{m}}{\mathrm{s}}, \Delta t = 5.0\ \mathrm{s}, a = 3.0\frac{\mathrm{m}}{\mathrm{s}^{2}}$.

So,

$$\Delta x = 4.47 \cdot 5.0 + \frac{1}{2} \cdot 3.0 \cdot 5.0^{2} = 59.85\ \mathrm{m}.$$

Then, the final speed is

$$v_{f} = v_{i} + a \Delta t = 4.47 + 3.0 \cdot 5.0 = 19.47\ \frac{\mathrm{m}}{\mathrm{s}}.$$

Answer: $19.47\frac{\mathrm{m}}{\mathrm{s}}$ and $59.85\ \mathrm{m}$.

http://www.AssignmentExpert.com/