Advertisements
Advertisements
प्रश्न
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. At what times the particle changes direction?
Advertisements
उत्तर
s = f(t) = 2t3 – 9t2 + 12t – 4
V = f'(t) = 6t2 – 18t + 12
V = 0 ⇒ 6(t2 – 3t – 2) = 0
(t – 1)(t – 2) = 0
t = 1, 2
When t < 1, (say t = 0.5)
V = 6(0.25 – 1.5 + 2) = +ve
When 1 < t < 2, (say t = 1.5)
V = 6(2.25 – 4.5 + 2) = – ve
When t > 2, (say t = 3)
V = 6(9 – 6 + 2) = +ve
So the particle changes its direction when t lies between 1 and 2 secs.
APPEARS IN
संबंधित प्रश्न
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. What is the average velocity with which the camera falls during the last 2 seconds?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the total distance travelled by the particle in the first 4 seconds
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the particle’s acceleration each time the velocity is zero
If the volume of a cube of side length x is v = x3. Find the rate of change of the volume with respect to x when x = 5 units
If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = `sqrt(3x)` then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres
A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shoreline. How fast is the beam moving along the shoreline when it makes an angle of 45° with the shore?
Find the tangent and normal to the following curves at the given points on the curve
y = x2 – x4 at (1, 0)
Find the tangent and normal to the following curves at the given points on the curve
y = x sin x at `(pi/2, pi/2)`
Find the tangent and normal to the following curves at the given points on the curve
x = cos t, y = 2 sin2t at t = `pi/2`
Find the equations of the tangents to the curve y = 1 + x3 for which the tangent is orthogonal with the line x + 12y = 12
Find the equations of the tangents to the curve y = `- (x + 1)/(x - 1)` which are parallel to the line x + 2y = 6
Find the angle between the rectangular hyperbola xy = 2 and the parabola x2 + 4y = 0
Show that the two curves x2 – y2 = r2 and xy = c2 where c, r are constants, cut orthogonally
Choose the correct alternative:
A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per second when the balloon is 30 metres above the ground
Choose the correct alternative:
A stone is thrown, up vertically. The height reaches at time t seconds is given by x = 80t – 16t2. The stone reaches the maximum! height in time t seconds is given by
Choose the correct alternative:
Find the point on the curve 6y = x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is
Choose the correct alternative:
The tangent to the curve y2 – xy + 9 = 0 is vertical when
