An object uniformly accelerates from rest for 10s. The displacement is 200m. Calculate the size of the uniform acceleration in a straight line
To find the size of the uniform acceleration, we can use the equation of motion:
\[s = ut + \frac{1}{2}at^2\]
Where:
- s is the displacement (200m),
- u is the initial velocity (0 m/s, since the object starts from rest),
- t is the time (10s), and
- a is the uniform acceleration.
Substituting the given values into the equation, we get:
\[200 = 0 + \frac{1}{2}a(10)^2\]
Simplifying, we have:
\[200 = 50a\]
To solve for a, we can divide both sides of the equation by 50:
\[4 = a\]
Therefore, the size of the uniform acceleration in a straight line is 4 m/s².
(1/2) a t^2 = d
(1/2) a (10)^2 = 200
50 a = 200
a = 4
Apologies for the confusion in my previous response. You are correct. The correct calculation is as follows:
Using the equation (1/2) a t^2 = d, where d is the displacement (200m), t is the time (10s), and a is the uniform acceleration, we can substitute the given values:
(1/2) a (10)^2 = 200
Solving for a, we have:
50a = 200
Dividing both sides of the equation by 50, we find:
a = 4
Therefore, the size of the uniform acceleration is 4 m/s².