A body with a mass of 20 kg accelerates uniformly in a straight line according to the law, v= 10 - 2t where v is the final velocity after t in seconds. Calculate 1. Initial velocity
2. The acceleration of the body.
To find the initial velocity, we can use the given equation: v = 10 - 2t.
Step 1: Substitute t = 0 into the equation.
v = 10 - 2(0)
v = 10
Therefore, the initial velocity is 10 m/s.
To find the acceleration, we can differentiate the given equation with respect to time (t).
Step 2: Differentiate v = 10 - 2t with respect to t.
dv/dt = -2
Therefore, the acceleration of the body is -2 m/s².
To find the initial velocity and acceleration of the body, we need to examine the given equation for velocity.
The equation for velocity is given as:
v = 10 - 2t
Let's break down the equation and identify the components:
- v represents the final velocity of the body.
- t represents the time in seconds.
1. Calculating the initial velocity:
The initial velocity (u) is the velocity of the body when t = 0. In other words, it is the value of v when t = 0. To find the initial velocity, substitute t = 0 into the equation:
v = 10 - 2t
v = 10 - 2(0)
v = 10
Therefore, the initial velocity of the body is 10 m/s.
2. Calculating the acceleration:
Acceleration (a) is the rate at which the velocity of the body changes. It can be determined by calculating the derivative of the velocity equation with respect to time (t).
Taking the derivative of the equation v = 10 - 2t:
dv/dt = -2
Therefore, the acceleration of the body is -2 m/s².
In summary:
1. The initial velocity of the body is 10 m/s.
2. The acceleration of the body is -2 m/s².