Answer:
 is the time taken by the car to accelerate the desired range of the speed from zero at full power.
  is the time taken by the car to accelerate the desired range of the speed from zero at full power.
Explanation:
Given:
Range of speed during which constant power is supplied to the wheels by the car is  .
.
- Initial velocity of the car,  
- final velocity of the car during the test,  
- Time taken to accelerate form zero to 32 mph at full power,  
- initial velocity of the car,  
- final desired velocity of the car,  
Now the acceleration of the car:



Now using the equation of motion:


 is the time taken by the car to accelerate the desired range of the speed from zero at full power.
 is the time taken by the car to accelerate the desired range of the speed from zero at full power.
 
        
             
        
        
        
Answer: 0.516 ft/s
Explanation:
Given 
Length of ladder L=20 ft
The speed at which the ladder moving away is v=2 ft/s
after 1 sec, the ladder is 5 ft away from the wall
So, the other end of the ladder is at 

Also, at any instant t

differentiate w.r.t.

 
        
             
        
        
        
Answer:
619.8 N
Explanation:
The tension in the string provides the centripetal force that keeps the rock in circular motion, so we can write:

where
T is the tension
m is the mass of the rock
v is the speed
r is the radius of the circular path
At the beginning,
T = 50.4 N
v = 21.1 m/s
r = 2.51 m
So we can use the equation to find the mass of the rock:

Later, the radius of the string is decreased to
r' = 1.22 m
While the speed is increased to
v' = 51.6 m/s
Substituting these new data into the equation, we find the tension at which the string breaks:
