A car of mass 550kg accelerates steadily from rest to 25m/s in 30s.
a). What is its acceleration?
b). What resultant force produces this acceleration?
c). The actual force will be greater, why?
I will be happy to check these for you, please show your thinking.
I think I have a little idea on Q.a) only.
F = ma
= 550 x 25
=13750N
so acceleration is
a = v - u/t
=25 - 0/30
=0.83 ms^-2
that's all i know. I don't know about Q.b and Q.c.
To find the answers to the given questions, we need to use the equations of motion and the concepts of force and acceleration.
a) What is its acceleration?
Acceleration (a) is the rate of change of velocity. We can calculate it using the equation:
a = (v - u) / t
where:
- a is the acceleration,
- v is the final velocity (25 m/s in this case),
- u is the initial velocity (0 m/s since the car starts from rest),
- t is the time taken (30 seconds).
Substituting the given values into the equation:
a = (25 m/s - 0 m/s) / 30 s
a = 25 m/s / 30 s
a ≈ 0.833 m/s²
Therefore, the acceleration of the car is approximately 0.833 m/s².
b) What resultant force produces this acceleration?
According to Newton's second law of motion, the force acting on an object is equal to its mass multiplied by its acceleration. The equation for force (F) is given by:
F = m * a
where:
- F is the resultant force,
- m is the mass of the object (550 kg),
- a is the acceleration (0.833 m/s²).
Substituting the given values into the equation:
F = 550 kg * 0.833 m/s²
F ≈ 457.15 N
Therefore, the resultant force producing this acceleration is approximately 457.15 N.
c) The actual force will be greater, why?
The actual force experienced by the car will be greater than 457.15 N because there are other forces acting on the car, such as friction and air resistance. These forces oppose the motion of the car and need to be overcome by a greater force to produce the acceleration mentioned earlier. Therefore, the actual force required will take into account the additional forces acting on the car.