1st derivative gives velocity;
d r(t)/ dt = 2t i + 6 j + 4/t k
2nd derivative gives acceleration;
d^2 r(t)/ dt^2 = 2 i - 4/ t^2
Speed ;
Square root of (4 t^2 + 36 + 16/ t^2)
For a given time, like 2 seconds, t will be 2. And answer of speed will be scalar.
There are two external force acts on the chair.
1. The force due to earth gravity, acts in the downward direction.
2. Reaction force of the gravity, which acts in the Upward direction (Normal Force).
On every object, there is a force acts due to gravity of earth, which pulls the object towards the centre of earth, known as gravity force, always acts in the downward direction. Mathematically it's given as
F=mg
here, m is the mass of the object, and g is the acceleration of gravity.
To balance this gravity force, a counter force acts in the opposite direction, whose magnitude is equal to the force of gravity
Explanation:
Mass of the ball, m = 0.058 kg
Initial speed of the ball, u = 11 m/s
Final speed of the ball, v = -11 m/s (negative as it rebounds)
Time, t = 2.1 s
(a) Let F is the average force exerted on the wall. It is given by :


F = 0.607 N
(b) Area of wall, 
Let P is the average pressure on that area. It is given by :


P = 0.202 Pa
Hence, this is the required solution.
Answer:
232.641374 mph
Explanation:
A race car has a maximum speed of 0.104km/s
Let X represent the speed in miles per hour
Therefore the speed in miles per hour can be calculated as follows
1 km/s = 2,236.936292 mph
0.104km/s = X
X = 0.104 × 2,236.936292
X = 232.641374
Hence the speed in miles per hour is 232.641374 mph