A body of mass 15kg is placed on a smooth plane which is inclined at 60° to the horizontal. Find:

a)the acceleration of the body as it moves down the plane
b)the velocity that the body attains after 5s if:
(i)it starts from rest and;
(ii)it moves with an initial velocity of 4m/s^2?

a) g * sin(60º)

b) (i) 5 s * g * sin(60º)

(ii) 4 m/s + [5 s * g * sin(60º)]

g is gravitational acceleration ... 9.8 m/s^2

a. Mg = 15*9.8 = 147 N. = Wt. of mass.

Fp = 147*sin60 = 127 N. = Force parallel to incline.
Fp = M*a
127 = 15a
a = 8.5 m/s^2.

b. V = Vo + a*T = 0 + 8.5*5 = ___ m/s.

V = Vo + a*T = 4 + 8.5*5 =

To find the solutions to your problem, we'll need to break it down into two parts:

a) Acceleration of the body as it moves down the plane:
The force acting down the plane is the component of the gravitational force parallel to the plane. This force can be calculated using the formula:

Force = m * g * sin(θ)

where m is the mass of the body, g is the acceleration due to gravity (approximately 9.8 m/s^2), and θ is the angle of the inclined plane (60° in this case). Substituting the values:

Force = 15 kg * 9.8 m/s^2 * sin(60°)

Force = 15 kg * 9.8 m/s^2 * 0.866

Force = 127.05 N

The net force acting on the body is equal to the mass times the acceleration, so:

Force = m * a

a = Force / m

a = 127.05 N / 15 kg

a = 8.47 m/s^2

Therefore, the acceleration of the body as it moves down the plane is 8.47 m/s^2.

b) Velocity the body attains after 5 seconds:
(i) If the body starts from rest, we can use the formula:

v = u + a * t

where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration (8.47 m/s^2), and t is the time (5 seconds).

v = 0 + 8.47 m/s^2 * 5s

v = 42.35 m/s

Therefore, the velocity that the body attains after 5 seconds starting from rest is 42.35 m/s.

(ii) If the body moves with an initial velocity of 4 m/s, we can use the same formula:

v = u + a * t

v = 4 m/s + 8.47 m/s^2 * 5s

v = 42.35 m/s

Therefore, the velocity that the body attains after 5 seconds starting with an initial velocity of 4 m/s is also 42.35 m/s.

To find the acceleration of the body as it moves down the plane, we need to resolve the force acting on the body along the inclined plane. There are two forces involved: the gravitational force (mg) acting vertically downwards and the component of the gravitational force parallel to the inclined plane, which we'll call the force of gravity along the plane (mg sinθ).

a) The acceleration (a) of the body can be found using Newton's second law of motion, which states that the net force on an object (Fnet) is equal to the product of its mass (m) and its acceleration (a) (Fnet = ma). In this case, Fnet is equal to the force of gravity along the plane (mg sinθ).

So we have:
Fnet = mg sinθ
ma = mg sinθ
a = g sinθ

Given that the mass of the body (m) is 15 kg and the angle of inclination (θ) is 60°, we can substitute these values into the equation to find the acceleration (a).

a = g sinθ
a = 9.8 m/s^2 * sin(60°)
a ≈ 8.49 m/s^2

Therefore, the acceleration of the body as it moves down the plane is approximately 8.49 m/s^2.

b) Now, let's calculate the velocity that the body attains after 5 seconds under two different scenarios:

(i) When the body starts from rest:
In this case, the initial velocity (u) is 0 m/s, and the final velocity (v) can be found using the equation v = u + at, where a is the acceleration determined in part (a) and t is the time.

v = u + at
v = 0 + (8.49 m/s^2) * 5 s
v ≈ 42.45 m/s

Therefore, the velocity that the body attains after 5 seconds, starting from rest, is approximately 42.45 m/s.

(ii) When the body moves with an initial velocity of 4 m/s:
In this case, the initial velocity (u) is 4 m/s, and we'll again use the equation v = u + at.

v = u + at
v = 4 m/s + (8.49 m/s^2) * 5 s
v ≈ 46.45 m/s

Therefore, the velocity that the body attains after 5 seconds, with an initial velocity of 4 m/s, is approximately 46.45 m/s.