Question

A dolphin accelerates for 2.0 sec from an initial speed of 7.5 m/sec in order to take a look at a dolphin of the opposite sex.Calculate the dolphin's final speed if the deceleration had a magnitude of 1.5 m/square seconds.

Answer 1

A dolphin accelerates for 2.0 sec from an initial speed of $7.5\,\mathrm{m/sec}$ in order to take a look at a dolphin of the opposite sex. Calculate the dolphin's final speed if the deceleration had a magnitude of $1.5\,\mathrm{m/square}$ seconds.

**Solution.**

$$t = 2s, v_0 = 7.5\,\frac{\mathrm{m}}{\mathrm{s}}, \quad a = 1.5\,\frac{\mathrm{m}}{\mathrm{s}^2};$$ $$v - ?$$

In the problem given that the dolphin is accelerating, but then in question says about deceleration of the dolphin.

In the situation when the dolphin accelerates from an initial speed to final speed, final speed is:

$$v = v_0 + a t.$$ $$v = 7.5 + 1.5 \cdot 2 = 10.5\,\left(\frac{\mathrm{m}}{\mathrm{s}}\right).$$

In the situation when the dolphin decelerates from an initial speed to final speed, final speed is:

$$v = v_0 - a t.$$ $$v = 7.5 - 1.5 \cdot 2 = 4.5\,\left(\frac{\mathrm{m}}{\mathrm{s}}\right).$$

**Answer:** The final speed of the dolphin is $v = 10.5\,\frac{\mathrm{m}}{\mathrm{s}}$ or $v = 4.5\,\frac{\mathrm{m}}{\mathrm{s}}$.