Final answer:
To find the magnitude of an object's acceleration given its displacement of 48m in 5.2s with a zero initial velocity, use the kinematic equation S = ut + ½at², resulting in an acceleration of approximately 3.55 m/s².
Step-by-step explanation:
The question involves calculating the magnitude of acceleration for an object moving with constant acceleration and a zero initial velocity that travels a certain distance over a given time. To find the acceleration, we can use the kinematic equation for uniformly accelerated motion, which is:
S = ut + ½at²
Where:
- S = displacement (48m)
- u = initial velocity (0 m/s, since it's given as zero)
- a = acceleration (which we need to find)
- t = time (5.2s)
Plugging in the known values, we get:
48m = (0 m/s)(5.2s) + ½a(5.2s)²
This simplifies to:
48m = ½a(27.04s²)
Now we solve for 'a' to find the acceleration:
a = (2 × 48m) / (27.04s²)
a = 96m / 27.04s²
a = 3.55 m/s² (approximately)
Therefore, the magnitude of the object's acceleration is 3.55 m/s².