Kinematics: Question 9

Worked solution

Step 1: Identify the known quantities

The go-kart has an initial velocity $u=4.0\text{ m s}^{-1}$, a uniform acceleration $a=2.0\text{ m s}^{-2}$, and this acts for a time $t=5.0\text{ s}$. The displacement is required, so the appropriate suvat equation is: $s = ut + \tfrac{1}{2}at^2$

Step 2: Substitute the values

$s = (4.0)(5.0) + \tfrac{1}{2}(2.0)(5.0)^2$ $s = 20 + \tfrac{1}{2}(2.0)(25)$ $s = 20 + 25$ $s = 45\text{ m}$

Why the other options are wrong

• B ($70\text{ m}$): comes from omitting the factor of $\tfrac{1}{2}$, calculating $20 + (2.0)(25) = 20+50=70$.
• C ($20\text{ m}$): comes from including only the $ut$ term and ignoring the acceleration’s contribution entirely.
• D ($25\text{ m}$): comes from including only the $\tfrac{1}{2}at^2$ term, as though the go-kart had started from rest rather than at $4.0\text{ m s}^{-1}$.

Final answer

• Displacement during the $5.0\text{ s}$ $= \boxed{45}\text{ m}$, option A.