Question

A blue shark accelerates at a rate of 16m/s for a time of 0.8s. During this time it travels a

distance of 11.52m. Calculate its initial speed.

Answer 1

The initial velocity of this shark is
`8.0\; \rm m \cdot s^(-1)`. (Assuming that the unit of the acceleration in this question is
`\rm m\cdot s^(-2)`.)

Step-by-step explanation:

Let
`a` denote the acceleration of this shark.

Let
`v_0` denote the initial velocity of this shark.

Assume that the acceleration
`a` of this shark is constant (as it is in this question.) Over a period of time
`t`, the shark would have travelled a distance of:

`\displaystyle x = (1)/(2)\, a\, t^2 + v_0\, t`.

This question states that:

• 
  `x = 11.52\; \rm m`,
• 
  `t = 0.8\; \rm s`. (That is: this shark travelled a distance of
  `11.52\; \rm m` in
  `0.8\; \rm s`.)
• 
  `a = 16\; \rm m \cdot s^(-2)` (the acceleration of this shark is indeed a constant.)

This question is asking for
`v_0`, the initial velocity of this shark at the beginning of this
`0.8`-second period. Substitute the three known values into the equation:

`\displaystyle 11.52 = (1)/(2)* 16* (0.8)^2 + 0.8\, v_0`.

Solve for
`v_0`:

`v_0 = \displaystyle (11.52 - (1/2) * 16 * (0.8)^2)/(0.8) = 8.0\; \rm m \cdot s^(-1)`.