A truck starts from rest and accelerates at
2.0 m/s² for 4.0 s. How far will it have gone at the end of this time?
(1/2) a t^2
To find the distance the truck will have gone at the end of 4.0 seconds, you can use the kinematic equation:
\[ d = v_i t + \frac{1}{2} a t^2 \]
where:
- \( d \) is the distance traveled
- \( v_i \) is the initial velocity (which is 0 in this case since the truck starts from rest)
- \( a \) is the acceleration of the truck (2.0 m/s²)
- \( t \) is the time (4.0 seconds)
Plugging in the values into the equation:
\[ d = 0 \cdot 4 + \frac{1}{2} \cdot 2.0 \cdot (4.0)^2 \]
Simplifying:
\[ d = 0 + 0.5 \cdot 2.0 \cdot 16 \]
\[ d = 0 + 1.0 \cdot 16 \]
\[ d = 16 \]
Therefore, the truck will have gone a distance of 16 meters at the end of 4.0 seconds.