This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Hey ibrahimrashidatu247, good to see you again. Here are the solutions to the questions: Question 31: To find the time taken, we use the kinematic equation for displacement. Given: Initial velocity u = 0 m/s (starts from rest) Displacement s = 98 m Acceleration a = 4 m/s^2 Step 1: Use the kinematic equation s = ut + (1)/(2)at^2. 98 = (0)t + (1)/(2)(4)t^2 Step 2: Simplify the equation. 98 = 2t^2 Step 3: Solve for t. t^2 = (98)/(2) t^2 = 49 t = sqrt(49) t = 7 s The correct option is A. The time taken is A. 7 sec. Question 32: To find the time taken, we use the kinematic equation for displacement. Given: Initial velocity u = 72 km/h Deceleration a = -1.5 m/s^2 Displacement s = 70 m Step 1: Convert initial velocity from km/h to m/s. u = 72 km/h × 1000 m1 km × 1 h3600 s u = 20 m/s Step 2: Use the kinematic equation s = ut + (1)/(2)at^2. 70 = (20)t + (1)/(2)(-1.5)t^2 70 = 20t - 0.75t^2 Step 3: Rearrange into a quadratic equation At^2 + Bt + C = 0. 0.75t^2 - 20t + 70 = 0 Step 4: Use the quadratic formula t = -B ± sqrt(B^2 - 4AC)2A. Here, A = 0.75, B = -20, C = 70. t = -(-20) ± sqrt((-20)^2 - 4(0.75)(70))2(0.75) t = 20 ± sqrt(400 - 210)1.5 t = 20 ± sqrt(190)1.5 t = (20 ± 13.784)/(1.5) Step 5: Calculate the two possible values for t. t_1 = (20 + 13.784)/(1.5) = (33.784)/(1.5) ≈ 22.52 s t_2 = (20 - 13.784)/(1.5) = (6.216)/(1.5) ≈ 4.144 s Since the car is slowing down, both times are physically possible if the car hasn't stopped and reversed within 70m. However, usually, the smaller positive time is the one sought in such problems before it potentially stops or reverses. Let's check the final velocity for t_2. v = u + at = 20 + (-1.5)(4.144) = 20 - 6.216 = 13.784 m/s. This is a valid positive velocity. The correct option is C. The time taken is C. 4.14 sec. Question 33: The phenomenon where a ball strikes the ground (action) and the ground pushes back with an equal and opposite force (reaction) is a direct application of Newton's Third Law of Motion. The correct option is C. The law of motion is C. third law. Question 34: The statement "the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object" is the definition of Newton's Second Law of Motion, often expressed as F = ma. The correct option is B. The name of this law of motion is B. second law. Question 35: When you touch something, you exert a force on it, and in response, the object exerts an equal and opposite force back on you. It is this reaction force that you feel. This interaction is explained by Newton's Third Law of Motion. The correct option is C. The law is C. third law. Question 36: Work done is calculated as the product of force and displacement in the direction of the force. Given: Force F = 10 N Displacement d = 4 m Step 1: Use the formula for work done W = F × d. W = 10 N × 4 m Step 2: Calculate the work done. W = 40 J The correct option is A. The work done is A. 40 J. Question 37: Work done to lift an object is equal to the force (weight) multiplied by the height lifted. Given: Work done W = 500 J Force (weight) F = 200 N Step 1: Use the formula for work done W = F × h. 500 J = 200 N × h Step 2: Solve for h. h = 500 J200 N h = 2.5 m The correct option is B. The height the weight was lifted is B. 2.5 m. Question 38: Power is the rate at which energy is transformed or transferred. Given: Energy E = 10,000 J Time t = 4 s Step 1: Use the formula for power P = (E)/(t). P = 10,000 J4 s Step 2: Calculate the power. P = 2500 W The correct option is B. The power is B. 2,500 W. Question 39: Energy transformed is the product of power and time. Given: Power P = 60 W Time t = 20 s Step 1: Use the formula for energy E = P × t. E = 60 W × 20 s Step 2: Calculate the energy transformed. E = 1200 J The correct option is A. The energy transformed is A. 1,200 J. Question 40: Kinetic energy is the energy an object possesses due to its motion. • A body at rest has zero kinetic energy. • A body in motion possesses kinetic energy. • Being placed on a platform does not inherently mean motion. • Zero gravity does not prevent motion or kinetic energy. The correct option is B. A body possesses kinetic energy in the state of B. Motion. Send me the next one 📸