Mathematics of Physics Questions

Questions to Try

Q1. TWO particles, 1 and 2 move with constant velocities v1 and v2 along two mutually perpendicular straight lines towards the intersection point O. At the moment t= 0 the particles were located at the distance L1 and L2 from the point O
How soon will the distance between the particles become the smallest? What is it
equal to?

Q2. A police Jeep Approaching a Right Angeled intersection from the north is chasing a. speeding car that has turned the corner and is now moving straight east When the jeep is 0.6 km north of the intersection and the ear is 0.8 km to the east the police determine with radar that the distance between them and the car is increasing at 20 KMPH . If the , Jeep is moving at 60 kmph at the instant of measurement.what is the speed of the car?

Q3. You are given a rod of length L The linear mass density is A. such that A = a + bx Here a and b are constants and the mass of the rod increases as x decreases Find the mass of the rod.

Q4. If the sum of two unit vectors is a unit vector, then find the magnitude of their difference.

Q5. A man traversed half the distance with a velocity v0 The remaining part of the distance was covered with velocity v1 for half the time and With velocity v2 for the other half of the time. Find the average speed of the man over the whole time of motion.

Q6. A particle starts moving rectilineariy at time t= 0 such that Its velocity v changes with time t according to the equation v= t^2 - t, where t is in seconds and v in m/s . Find the time interval for which the particle retards.

Q7. In a car race, car A takes a time of t sec less than car B at the finish and passes the finishing point With a velocity v more than car B. Assuming that the cars Start from rest and travel with constant accelerations a1 and a2, respectively, show that v = √a1√a2√t .

Q8. A body is thrown vertically upwards from, the top of a tower. It reaches the ground in time t1. If it is thrown vertically downwards from the top of tower with the same speed it reaches the ground in time t2. If it is allowed to fall freely from same height, then find the time it takes to reach the ground. 

Q9. A balloon starts rising upwards With constant acceleration a and after time t a packet is dropped from it which reaches the ground after t seconds of dropping. Determine the value of t.

Q10. The relation between time t and distance x is t = ax^2 + bx Where a and b are constants. The retardation is 
a. 2av^3 
b. 2bv^3 
c. 2abv^3
d. 2b^2v^3 

Q11. The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation t = √x +3 , where x is in meters and t is in seconds. Find the displacement of the particle when its velocity is zero. 
a. Zero 
b. 12m 
c. 6m 
d. 18m 

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