To solve this problem, we can break it down into two parts: the initial acceleration phase and the subsequent deceleration phase. Let's calculate the magnitude of the deceleration.
First, let's find the final velocity at the end of the initial acceleration phase using the formula:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (0 m/s as the body starts from rest)
- a is the acceleration (6 m/s²)
- t is the time (8 seconds)
Plugging in the values, we have:
v = 0 + (6 m/s²)(8 s) v = 48 m/s
Next, we can find the acceleration during the deceleration phase using the formula:
a = (v - u) / t
where:
- a is the acceleration (which we need to find)
- v is the final velocity (48 m/s)
- u is the initial velocity (48 m/s since the body starts at rest)
- t is the time (5 seconds)
Plugging in the values, we have:
a = (48 m/s - 0 m/s) / 5 s a = 48 m/s / 5 s a = 9.6 m/s²
Therefore, the magnitude of the deceleration is 9.6 m/s².