Physics

The correct statement is: Between t = 1s and t = 10s, the direction of the acceleration is opposite to the direction of its velocity.

From 0 to 10s, the graph starts at x=1 and curves upwards as time progresses. The slope of the tangent to the curve at any point is positive, which means the velocity of the object is positive. As time goes on, the slope of the tangent to the curve becomes less steep. So, the magnitude of the velocity is decreasing. This implies that the acceleration a<0. Thus, the acceleration is in the opposite direction of the velocity. This statement is correct.

Analyze other statements:

Option A: At t = 10s, the object's speed is maximum.

The slope of the x-t graph represents the velocity. At t = 10s, the slope of the graph is 0 (the tangent to the curve at t = 10s is horizontal). Since speed is the magnitude of velocity, the speed is 0 at t = 10s, not maximum. So, this statement is incorrect.

Option C: At t = 8s and t = 12s, the direction of the object's acceleration is opposite.

From 0 to 10s, the acceleration a<0 (negative direction).

From 10s to 20s, the graph starts at a positive position value and curves downwards as time increases. The slope of the tangent to the curve at any point is negative, which means the velocity of the object is negative. As time progresses, the slope of the tangent to the curve becomes steeper (in magnitude). So, the magnitude of the velocity is increasing. This implies that the acceleration is in the same direction of the velocity. It's in negative direction.

Thus, the acceleration has the same direction at t = 8s and t = 12s. This statement is incorrect.

Option D: From 0 to 20s, the object's displacement is 9 meters.

The initial position at t = 0 is and the final position at t = 20 s is

Click "Show Answer" to reveal the answer and analysis